Problem: Solve for $x$ and $y$ using elimination. ${x+6y = 16}$ ${-x+5y = -5}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $11y = 11$ $\dfrac{11y}{{11}} = \dfrac{11}{{11}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x+6y = 16}\thinspace$ to find $x$ ${x + 6}{(1)}{= 16}$ $x+6 = 16$ $x+6{-6} = 16{-6}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {-x+5y = -5}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(1)}{= -5}$ ${x = 10}$